MHT CET · Maths · Probability
If is observed that \(25 \%\) of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that at least 5 of them will be solved is
- A \(\frac{19}{1024}\)
- B \(\frac{19}{4096}\)
- C \(\left(\frac{1}{4}\right)^6\)
- D \(\frac{19}{2048}\)
Answer & Solution
Correct Answer
(B) \(\frac{19}{4096}\)
Step-by-step Solution
Detailed explanation
We have probability of cases getting solved \(=25 \%=\frac{1}{4}\)
\(\mathrm{p}=\frac{1}{4} \Rightarrow \mathrm{q}=\frac{3}{4}\) and we have \(\mathrm{n}=6, \mathrm{x}=5,6\)
Hence required probability
\(=\left[{ }^6 \mathrm{C}_5\left(\frac{1}{4}\right)^5\left(\frac{3}{4}\right)^1\right]+\left[{ }^6 \mathrm{C}_6\left(\frac{1}{4}\right)^6\left(\frac{3}{4}\right)^0\right] \)
\( =\frac{(6)(3)}{(4)^6}+\frac{1}{(4)^6}=\frac{19}{(4)^6}=\frac{19}{4096} \)
\(\mathrm{p}=\frac{1}{4} \Rightarrow \mathrm{q}=\frac{3}{4}\) and we have \(\mathrm{n}=6, \mathrm{x}=5,6\)
Hence required probability
\(=\left[{ }^6 \mathrm{C}_5\left(\frac{1}{4}\right)^5\left(\frac{3}{4}\right)^1\right]+\left[{ }^6 \mathrm{C}_6\left(\frac{1}{4}\right)^6\left(\frac{3}{4}\right)^0\right] \)
\( =\frac{(6)(3)}{(4)^6}+\frac{1}{(4)^6}=\frac{19}{(4)^6}=\frac{19}{4096} \)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The focal distance of a point on the parabola \(y^{2}=16 x\) whose ordinate is twice the abscissa, isMHT CET 2008 Easy
- If the curves \(y^2=6 x\) and \(9 x^2+\) by \(^2=16\) intersect each other at right angles, then the value of b isMHT CET 2025 Medium
- If \(y=\left((x+1)(4 x+1)(9 x+1) \ldots\left(\mathrm{n}^2 x+1\right)\right)^2\), then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) at \(x=0\) isMHT CET 2024 Easy
- The equation \(x^2-3 x y+2 y^2+3 x-5 y+2=0\) represents a pair of straight lines. If \(\theta\) is the angle between them, then the value of \(\cos \theta\) is equal toMHT CET 2025 Medium
- If general solution of \(\cos ^2 \theta-2 \sin \theta+\frac{1}{4}=0\) is \(\theta=\frac{\mathrm{n} \pi}{\mathrm{A}}+(-1)^{\mathrm{n}} \frac{\pi}{\mathrm{B}}, \mathrm{n} \in \mathrm{Z}\), then \(\mathrm{A}+\mathrm{B}\) has the valueMHT CET 2023 Hard
- Bacteria increases at the rate proportional to the number of bacteria present. If the original number N doubles in 4 hours, then the number of bacteria will be \(4 \mathrm{~N}\) inMHT CET 2020 Easy
More PYQs from MHT CET
- Two springs of spring constants ' \(\mathrm{K}^{\prime}\) and ' \(2 \mathrm{~K}^{\prime}\) are stretched by same force. If ' \(\mathrm{w}_{1}{ }^{\circ}\) and ' \(\mathrm{w}_{2}\) ' are the energies stored in them respectively thenMHT CET 2020 Medium
- Which of the following oxyacid of chlorine has highest thermal stability?MHT CET 2020 Medium
- The eccentricity of the hyperbola which passes through the points \((3,0)\) and \((3 \sqrt{2}, 2)\) isMHT CET 2025 Medium
- Which of the following compounds reacts immediately with Lucas reagent?MHT CET 2018 Medium
- The equation of the circle which passes through the centre of the circle \(x^2+y^2+8 x+10 y-7=0\) and concentric which the circle \(2 x^2+2 y^2-8 x-12 y-9=0\) isMHT CET 2024 Easy
- The maximum value of \(x y\) when \(x+2 y=8\) isMHT CET 2023 Easy